No one knows lol
Live Chess and Play Online?
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The closest to an answer I could find is this:
They're conceptually the same thing. "Live Chess" is the established version of the feature, and "Play" is the new beta version of the feature that will eventually fully replace the previous version. For now, they're both available while the kinks in the new version are worked out.
Source: Differences between Online Chess and Live Chess
What's the difference between Live Chess and Play Online here in chess.com?